Some Studies On Weakly Semiprime Submodules And Commutativity Of Semiprime Rings

In this thesis, we mainly give some characterizations of weakly semiprime submodules and some results about commutativity of semiprime rings. We divide the thesis into three chapters.The first chapter is introduction. In this chapter, we have attempted to outline the importance of ring theories and module theories in algebras, and introduce the subjects connecting with our work.In chapter 2, we first give the concept of "n' —system", then we give some characterizations and relevant properties of weakly semiprime submodules, and investigate some properties of weakly semiprime ideals. At last , we summarize the concepts about prime and the relationship between them.In chapter 3, we mainly give some characterizations of commutativity of semiprime rings and partly summarize some results about commutativity of semiprime rings which have been studied from the 1990s up to now.